Comment by hnlmorg
5 hours ago
This is probably a dumb question, but do we actually know that pi has an infinite number of decimal digits or are we assuming that it does because we haven’t developed a sufficiently powerful computer to calculate the last digit of pi?
I’m guessing this is something that could be formally proven?
Here is a one page proof that pi is irrational - https://heuklyd.github.io/papers/pdf/Niven-1947.pdf
For a superb explanation of Niven's proof (which leaves more questions than answers when you first read it), I like Michael Penn's video: https://youtu.be/dFKbVTHK4tU?is=d2DbV5HDP0IpP9tA ....notwithstanding the length of the proof, this is quite a hard problem.
Thanks for the PDF. I feel like I understand even less now than I did before.
Thanks for sharing. That’s a nice read. I’m glad I asked :)
It's amazing how inscrutable calculus can be when you return to reading it after not doing so for a period of time, much like lisp or forth. I don't think I've actually done an integral or taken a derivative in years. I can see the elegance of that proof but I'll be damned if I can actually follow the mathematics from one step to the next.
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We definitely know that Pi is irrational, we just don't know if it's normal (i.e. if the PiFS joke even works).
Well, that should get GPT-5.5 extended thinking going for a few weeks.